Fast Algorithms for 1D Discrete Hartley Transform

2004 ◽  
pp. 93-144
Author(s):  
Guoan Bi ◽  
Yonghong Zeng
Keyword(s):  
Fast Algorithms ◽  
Discrete Hartley Transform ◽  
Hartley Transform

FAST DHT ALGORITHMS FOR COMPOSITE SEQUENCE LENGTHS

1998 ◽  
Vol 08 (03) ◽  
pp. 421-434
Author(s):  
GUOAN BI ◽  
YANQIU CHEN
Keyword(s):  
Fourier Transforms ◽  
Fast Algorithms ◽  
Sequence Length ◽  
Discrete Fourier Transforms ◽  
One Dimensional ◽  
Discrete Hartley Transform ◽  
Hartley Transform ◽  
Computational Structure ◽  
The One

This paper presents fast algorithms for the computation of discrete Hartley transform (DHT). When the sequence length N = p*q, where p and q are integers and relatively prime, the one dimensional DHT can be decomposed into p length-q DHT's and q length-p discrete Fourier transforms (DFT). Compared to other reported algorithms, the proposed one has a regular computational structure, provides flexibility for composite sequence lengths and achieves substantial savings on the required number of operations.

FAST ALGORITHMS FOR GENERALIZED DISCRETE HARTLEY TRANSFORM

2000 ◽  
Vol 10 (01n02) ◽  
pp. 77-83 ◽  
Author(s):  
GUOAN BI ◽  
SHOUTIAN LIAN
Keyword(s):  
Substantial Reduction ◽  
Fast Algorithms ◽  
Mapping Method ◽  
Discrete Hartley Transform ◽  
Type Iii ◽  
Hartley Transform ◽  
Simple Index ◽  
Index Mapping ◽  
Factor Decomposition ◽  
P Type

Based on the prime factor decomposition, this paper presents fast algorithms for type-III generalized discrete Hartley transform (GDHT). When N = p*q, where p and q are mutually prime, the length-N GDHT can be decomposed into p length-q type-III GDHT and q length-p type-III discrete cosine transform (DCT). The proposed algorithms achieve a substantial reduction of the number of additions and multiplications and possess a regular computational structure. In particular, a simple index mapping method is proposed to minimize the overall implementation complexity and cost.

Genetic-Algorithm-Based Optimization of Fragile Watermarking in Discrete Hartley Transform Domain

2016 ◽  
pp. 103-127
Author(s):  
Sudipta Kr Ghosal ◽  
Jyotsna Kumar Mandal
Keyword(s):  
Genetic Algorithm ◽  
Color Images ◽  
Fragile Watermarking ◽  
Transform Domain ◽  
One Dimensional ◽  
Discrete Hartley Transform ◽  
Hartley Transform ◽  
Message Digest ◽  
Simulation Results ◽  
Watermarking Scheme

In this chapter, a fragile watermarking scheme based on One-Dimensional Discrete Hartley Transform (1D-DHT) has been proposed to verify the authenticity of color images. One-Dimensional Discrete Hartley Transform (1D-DHT) converts each 1 x 2 sub-matrix of pixel components into transform domain. Watermark (along with a message digest MD) bits are embedded into the transformed components in varying proportion. To minimize the quality distortion, genetic algorithm (GA) based optimization is applied which yields the optimized component corresponding to each embedded component. Applying One-Dimensional Inverse Discrete Hartley Transform (1D-IDHT) on 1 x 2 sub-matrices of embedded components re-generates the pixel components in spatial domain. The reverse approach is followed by the recipient to retrieve back the watermark (along with the message digest MD) which in turn is compared against the re-computed Message Digest (MD') for authentication. Simulation results demonstrate that the proposed technique offers variable payload and less distortion as compared to existing schemes.

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